1. **State the problem:** Evaluate the limit $$\lim_{x \to 2^-} \frac{x^2 - 4x + 3}{x - 1}$$. 2. **Recall the formula and rules:** The limit of a rational function as $x$ approaches a value can often be found by direct substitution if the function is defined at that point. If direct substitution leads to an indeterminate form, factorization or simplification is needed. 3. **Simplify the expression:** Factor the numerator: $$x^2 - 4x + 3 = (x - 1)(x - 3)$$ So the expression becomes: $$\frac{(x - 1)(x - 3)}{x - 1}$$ 4. **Cancel common factors:** For $x \neq 1$, we can cancel $x - 1$: $$\frac{(x - 1)(x - 3)}{x - 1} = x - 3$$ 5. **Evaluate the limit:** Now, as $x$ approaches 2 from the left, $$\lim_{x \to 2^-} (x - 3) = 2 - 3 = -1$$ 6. **Conclusion:** The limit is $-1$. **Final answer:** $-1$